How Do You Construct a Triangle of Forces?

[riddle]

What's a "triangle of forces" (triforce, lol)

I've attached a snip from my textbook. I don't get how they make that triangle, and how they get those angles. Can someone please help.

 

[HallsofIvy]

The "7 N" force is set to be vertical since it is the gravitational force on an object.
The "A, B, P" diagram shows that vector $T_A$ is at 30 degrees to the horizontal and so is at 90- 30= 60 degrees to the vertical. That's where they get the angle at the bottom of the triangle. The vector $T_B$ is at 40 degrees to the horizontal and so is at 90- 40= 50 degrees to the vertical. That's where they get the angle at the top of the triangle. Of course, the angles in any triangle add to 180 degrees so the third angle in the triangle is 180- 60- 50= 70 degrees, the last angle in the triangle.

 

[gerben]

They just translated the force vectors a bit, they drew the Ta force vector at the end of the downward force vector and the Tb force vector at the end of the Ta force vector.

Because the Ta vector makes an angle of 30deg with the horizontal it makes an angel of 90-30=60deg with the vertical. A similar arguments gives the angle of Tb with the vertical

 

[riddle]

Oooh. So I guess that these are "free vectors".

EDIT: From Gerbens reply I'll take it as a yes, since they can be moved around.
Thanks guys.

 

[gerben]

A vector is a thing that has only length and direction, nothing else.

 

[HallsofIvy]

Oooh. So I guess that these are "free vectors".

EDIT: From Gerbens reply I'll take it as a yes, since they can be moved around.
Thanks guys.

That is true of all vectors.